/* Medium
A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach
    the bottom-right corner of the grid (marked 'Finish' in the diagram below).
        start
        +---------+----+----+----+----+----+
        |----|    |    |    |    |    |    |
        |----|    |    |    |    |    |    |
        +----------------------------------+
        |    |    |    |    |    |    |    |
        |    |    |    |    |    |    |    |
        +----------------------------------+
        |    |    |    |    |    |    |----|
        |    |    |    |    |    |    |----|
        +----+----+----+----+----+---------+
                                    finish
How many possible unique paths are there?


Above is a 7 x 3 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

Example 1:

Input: m = 3, n = 2
Output: 3
Explanation:
From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
1. Right -> Right -> Down
2. Right -> Down -> Right
3. Down -> Right -> Right
Example 2:

Input: m = 7, n = 3
Output: 28

Relatives:
62. Unique Paths
63. Unique Paths II
980. Unique Paths III
64. Minimum Path Sum
174. Dungeon Game
741. Cherry Pickup */

class Solution {
public:
    int uniquePaths(int m, int n) {
        vector<int> vec(n, 1);
        for (int row = 1; row < m; ++row) {
            for (int col = 1; col < n; ++col)
                vec[col] += vec[col-1];
        }

        return vec.back();
    }
};
